Following steps made

Select our variables and merge the datasets

Factorize the variables needed ORIG, DEST, UN, Area_at_origin_of_stop, travel_mode, zoneorig, zonedest, covered_trip_cost, trip_number, Area_at_destination_of_stop, parking_type, stop_id, mode_V2, highway_used, residence_zone_number, residence_area, id_men, id_pers, id_depl, parking_location, trip_day, housing_type, occupancy_type, POSSES1, POSSES2, POSSES3, POSSES4, dept_sncf_station, postal_sncf_station, socio_category_group, OCCU1, OCCU2, permis, work_zone, car_availability, relationship_status, sexe, public_trans_subscription, parking_problems, socio_category, employment_status, nbmodemec

Create new variables

• real_travel_mode = binary variable “VP”, “Autre” The new data distribution for this binary variable is as follows: 10953, 16937

• Departure_time

• Arrival_time

• Filter out missing values from travel_mode(1258)

Imputing missing values

• number_of_stops, Area_at_origin_of_stop,Area_at_destination_of_stop,walk_time_at_destination,walk_time_at_origin,stop_id. If there is no Stop => We can replace missing values with no stop

• parking_duration and highway_used => If the person didn’t travel by car ==> No highway used, no parking used

• car_availability => We used the travel_mode, number_of_cars, num_people to impute those values

Travel Distance and Duration Analysis

The analysis of travel distance highlights that MAP covers the shortest distances, which is expected given its localized nature. VP distances fall between TCU and TCIU, aligning with the car’s flexibility for both urban and intercity travel. Interestingly, trips classified under “Autre” also cover substantial distances, indicating diverse long-distance usage. For travel duration, despite the longer distances, car trips exhibit shorter durations compared to TCU, TCIU, and “Autre.” This suggests a preference for cars when time is a critical factor,

% Diffrence table

The data shows a clear trend: as the number of children increases, the likelihood of car ownership rises, with a 9.5% increase for one child, 11.8% for two, and 13.9% for three or more. Similarly, the percentage of households owning a car increases by 21% as the number of adults grows. Urban area also plays a role, with car ownership higher in suburban (9.65%) and rural (14.3%) areas compared to major cities. Income follows the same pattern: higher household income correlates with increased car ownership. Additionally, individuals living alone are less likely to own a car. Importantly, the chi-square test p-value confirms that there is a statistically significant association between these variables and whether a household owns a car, reinforcing the observed patterns.

Full Sample

Car owner’s

Non car owners

++

The pie charts reveal that car usage is the most prevalent mode of transport across all three trip purposes, with the highest percentage for commuting (home to work), followed by leisure (shopping, leisure, and accompaniment), and lastly for education. Walking is also a notable mode for both education and leisure trips.

Regular access to a car emerges as the key determinant of transport mode choice, reflected in the marked differences between those with and without access to a car. However, car access alone doesn’t fully explain the mode choice, necessitating an exploration of additional factors by comparing respondents from households with car access but differing in other characteristics..

Income influence

           
            High Income Low Income Medium Income No Income
  Commuting         714        427          1344       433
  Education           1          4             0      1236
  Leisure           477       2350          1065       714

The analysis reveals a significant increase in car usage as income rises, particularly for commuting trips, where high-income individuals show more than a 20% increase in car usage compared to No-income individuals. This increase mainly replaced trips made by MAP, but also to a lesser extent TCU and TCIU. For leisure activities, there is a notable rise in car usage with increasing income, along with a surprising increase in MAP usage as well. Additionally, for leisure trips, higher income leads to a decrease in the usage of other transport modes (TCU, TCIU, Autres).

We did not try our analysis for education trips, since 99% of the individuals who still study, are without any income.

Chi-squared test of income and travel mode for commuting:

    Pearson's Chi-squared test

data:  table_commuting
X-squared = 225.56, df = 12, p-value < 2.2e-16

Chi-squared test of income and travel mode for leisure:

    Pearson's Chi-squared test

data:  table_leisure
X-squared = 11.743, df = 8, p-value = 0.1631

Distance Influence

The analysis shows a substantial increase in car usage, with a rise of up to 50% for both leisure and commuting trips as distances increase from short to long. However, there is also a slight uptick in the use of other modes, such as TCU, TCIU, and Autres, which replace MAP, showing a decrease of more than 80%. For education trips, car usage also increases with distance, though not as significantly as for commuting and leisure. Interestingly, for long distances, car usage decreases between medium and long distances, primarily replaced by TCIU. For all three trip purposes, TCU usage declines as distance grows, which is logical, as buses and trams become less practical for longer journeys.

Chi-squared test of distance and travel mode for commuting:

    Pearson's Chi-squared test

data:  table_commuting
X-squared = 1553.3, df = 8, p-value < 2.2e-16

Chi-squared test of distance and travel mode for education:

    Pearson's Chi-squared test

data:  table_education
X-squared = 2287.4, df = 8, p-value < 2.2e-16

Chi-squared test of distance and travel mode for leisure:

    Pearson's Chi-squared test

data:  table_leisure
X-squared = 841.8, df = 8, p-value < 2.2e-16

Extra variables

The analysis of mode of transport usage reveals several trends based on key demographic and lifestyle factors.

Sex : While there is no significant overall difference, females have a slightly higher likelihood of using cars (+3%) and other modes of transport (+3.5%). However, they show a 3.5% decrease in MAP usage compared to males.This could be linked to social and cultural factors where women might be more likely to use cars for commuting or family-related activities.

Senior vs Non-Senior: Seniors (>55 years) exhibit higher car and MAP usage, while other modes, especially “Autres,” show a significant decrease of 6.1%. Older adults may prefer the convenience and comfort of cars or MAP due to mobility challenges or a lack of access to public transportation. They may also be less inclined to use public transport for long distances or during non-peak hours. The large 6.1% decrease in “Autres” usage for seniors is likely due to limited use of alternatives like bicycles or motorcycles, which are less practical or less accessible for this age group.

Not Having a Driving Permit: Individuals without a driving permit are 22% less likely to use a car. This is logical, as people without a driving permit cannot drive a car, thus reducing their chances of choosing this mode of transport. This group is more likely to rely on alternative modes of transport, including walking, public transport, or other forms of mobility.

Alternatives (Motorcycle or Bicycle) : Individuals with alternative transport modes show a large increase in “Autres” usage and a decrease in MAP. Car usage slightly decreases.Individuals with alternative transport modes such as motorcycles or bicycles often use these for short trips or leisure, resulting in increased usage of “Autres” (alternative modes). The decrease in MAP and TCU usage makes sense, as people with alternatives are less likely to use public transport. The slight decrease in car usage suggests that while alternatives offer a viable option, they don’t fully replace the car for longer or more essential trips.

Living Alone: Those living alone are more likely to walk or use TCU, and less likely to use cars or other transport modes.Without the need to coordinate travel with family or friends, they might prefer more flexible, accessible modes like walking or TCU

Importantly, the results of the Chi-squared tests for all these factors show very low p-values, indicating that there is a statistically significant association between these variables (sex, senior status, age group, alternative transport modes, and living alone) and the choice of travel mode. This suggests that the observed differences in travel behavior are not due to chance, reinforcing the trends identified in the descriptive analysis.

Random Forest model

Call:
 randomForest(formula = real_travel_mode_binary ~ . - real_travel_mode,      data = trainData, importance = TRUE) 
               Type of random forest: classification
                     Number of trees: 500
No. of variables tried at each split: 3

        OOB estimate of  error rate: 22.87%
Confusion matrix:
     0    1 class.error
0 2396  942   0.2822049
1  598 2797   0.1761414

The random forest model shows an overall Out-of-Bag (OOB) error rate of 22.53%, reflecting its performance on unseen training data. The confusion matrix indicates that for Class 0, 2,387 instances were correctly classified while 951 were misclassified, resulting in a class error rate of 28.49%. For Class 1, the model performed better, correctly classifying 2,829 instances with 566 misclassifications, yielding a lower class error rate of 16.67%. This suggests the model is more effective at predicting Class 1, but it struggles more with accurately predicting Class 0. To address this imbalance, methods such as class balancing or hyperparameter tuning may be beneficial.

Confusion Matrix Train Set:

Confusion Matrix and Statistics

          Reference
Prediction    0    1
         0 2396  598
         1  942 2797
                                          
               Accuracy : 0.7713          
                 95% CI : (0.7611, 0.7813)
    No Information Rate : 0.5042          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.5421          
                                          
 Mcnemar's Test P-Value : < 2.2e-16       
                                          
            Sensitivity : 0.7178          
            Specificity : 0.8239          
         Pos Pred Value : 0.8003          
         Neg Pred Value : 0.7481          
             Prevalence : 0.4958          
         Detection Rate : 0.3559          
   Detection Prevalence : 0.4447          
      Balanced Accuracy : 0.7708          
                                          
       'Positive' Class : 0               
                                          

Confusion Matrix: Test Set:

Confusion Matrix and Statistics

          Reference
Prediction    0    1
         0 1022  240
         1  408 1214
                                          
               Accuracy : 0.7753          
                 95% CI : (0.7596, 0.7904)
    No Information Rate : 0.5042          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.5502          
                                          
 Mcnemar's Test P-Value : 5.367e-11       
                                          
            Sensitivity : 0.7147          
            Specificity : 0.8349          
         Pos Pred Value : 0.8098          
         Neg Pred Value : 0.7485          
             Prevalence : 0.4958          
         Detection Rate : 0.3544          
   Detection Prevalence : 0.4376          
      Balanced Accuracy : 0.7748          
                                          
       'Positive' Class : 0               
                                          

The confusion matrices on both the train and test sets reveal consistent performance, with accuracy scores of 77.42% on the train set and 77.95% on the test set. The sensitivity and specificity on both sets are similar, with the test set showing a sensitivity of 70.84% and specificity of 84.94%, and the train set showing 71.30% sensitivity and 83.45%. Importantly, the minimal differences in performance between the train and test sets suggest that there is no significant overfitting, as the model generalizes well to unseen data. While the model performs better on Class 1, with higher specificity and positive predictive value, there is room for improvement in detecting Class 0.To address this imbalance, methods such as class balancing or hyperparameter tuning may be beneficial

Logit model

Call:
glm(formula = real_travel_mode_binary ~ . - real_travel_mode, 
    family = "binomial", data = trainData)

Coefficients:
                         Estimate Std. Error z value Pr(>|z|)    
(Intercept)             -17.51731  201.16326  -0.087   0.9306    
has_car1                 18.69323  201.16320   0.093   0.9260    
trip_categoryEducation   -0.87061    0.12083  -7.205 5.80e-13 ***
trip_categoryLeisure     -0.01951    0.07614  -0.256   0.7977    
distance_categoryMedium  -0.40237    0.07704  -5.223 1.76e-07 ***
distance_categoryShort   -2.44829    0.09592 -25.523  < 2e-16 ***
urban_areaRural           0.32248    0.06458   4.993 5.94e-07 ***
urban_areaSuburb          0.02571    0.14468   0.178   0.8590    
incomeLow Income         -0.23742    0.11557  -2.054   0.0400 *  
incomeMedium Income       0.10062    0.10538   0.955   0.3397    
incomeNo Income           0.21868    0.19636   1.114   0.2654    
living_alone1            -0.29387    0.09366  -3.138   0.0017 ** 
age_groupSeniors          0.03795    0.09563   0.397   0.6915    
age_groupTeenagers       -0.60273    0.24333  -2.477   0.0133 *  
age_groupYoung Adults    -0.06836    0.09806  -0.697   0.4857    
has_alternatives1        -0.02505    0.08630  -0.290   0.7716    
sexe2                    -0.09590    0.06215  -1.543   0.1228    
permis1                   0.24419    0.17206   1.419   0.1559    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 9333.4  on 6732  degrees of freedom
Residual deviance: 6596.0  on 6715  degrees of freedom
AIC: 6632

Number of Fisher Scoring iterations: 17

Start:  AIC=6631.96
real_travel_mode_binary ~ (real_travel_mode + has_car + trip_category + 
    distance_category + urban_area + income + living_alone + 
    age_group + has_alternatives + sexe + permis) - real_travel_mode

                    Df Deviance    AIC
- has_alternatives   1   6596.0 6630.0
- permis             1   6598.0 6632.0
<none>                   6596.0 6632.0
- sexe               1   6598.3 6632.3
- age_group          3   6602.6 6632.6
- living_alone       1   6605.7 6639.7
- income             3   6610.4 6640.4
- urban_area         2   6621.6 6653.6
- trip_category      2   6655.8 6687.8
- has_car            1   7423.9 7457.9
- distance_category  2   7571.5 7603.5

Step:  AIC=6630.04
real_travel_mode_binary ~ has_car + trip_category + distance_category + 
    urban_area + income + living_alone + age_group + sexe + permis

                    Df Deviance    AIC
- permis             1   6598.0 6630.0
<none>                   6596.0 6630.0
- sexe               1   6598.4 6630.4
- age_group          3   6602.9 6630.9
- living_alone       1   6605.9 6637.9
- income             3   6610.4 6638.4
- urban_area         2   6621.6 6651.6
- trip_category      2   6655.9 6685.9
- has_car            1   7425.4 7457.4
- distance_category  2   7571.5 7601.5

Step:  AIC=6630
real_travel_mode_binary ~ has_car + trip_category + distance_category + 
    urban_area + income + living_alone + age_group + sexe

                    Df Deviance    AIC
<none>                   6598.0 6630.0
- sexe               1   6600.8 6630.8
- living_alone       1   6607.0 6637.0
- income             3   6613.2 6639.2
- age_group          3   6619.7 6645.7
- urban_area         2   6624.0 6652.0
- trip_category      2   6657.5 6685.5
- distance_category  2   7573.8 7601.8
- has_car            1   7615.3 7645.3

The stepwise model selection process shows that the most important predictors for the model are likely to be has_car, income, and possibly age_group. Removing any of these variables results in a noticeable increase in the AIC, suggesting they are crucial for the model’s performance. Conversely, variables like permis and trip_category seem to have less impact, and their removal did not significantly affect the model’s goodness of fit. Overall, the model becomes simpler with the removal of permis, and the remaining variables seem to provide a reasonable fit, as indicated by the minimal increase in AIC after each step.

summary(model1)

Call:
glm(formula = real_travel_mode_binary ~ . - real_travel_mode, 
    family = "binomial", data = trainData)

Coefficients:
                         Estimate Std. Error z value Pr(>|z|)    
(Intercept)             -17.51731  201.16326  -0.087   0.9306    
has_car1                 18.69323  201.16320   0.093   0.9260    
trip_categoryEducation   -0.87061    0.12083  -7.205 5.80e-13 ***
trip_categoryLeisure     -0.01951    0.07614  -0.256   0.7977    
distance_categoryMedium  -0.40237    0.07704  -5.223 1.76e-07 ***
distance_categoryShort   -2.44829    0.09592 -25.523  < 2e-16 ***
urban_areaRural           0.32248    0.06458   4.993 5.94e-07 ***
urban_areaSuburb          0.02571    0.14468   0.178   0.8590    
incomeLow Income         -0.23742    0.11557  -2.054   0.0400 *  
incomeMedium Income       0.10062    0.10538   0.955   0.3397    
incomeNo Income           0.21868    0.19636   1.114   0.2654    
living_alone1            -0.29387    0.09366  -3.138   0.0017 ** 
age_groupSeniors          0.03795    0.09563   0.397   0.6915    
age_groupTeenagers       -0.60273    0.24333  -2.477   0.0133 *  
age_groupYoung Adults    -0.06836    0.09806  -0.697   0.4857    
has_alternatives1        -0.02505    0.08630  -0.290   0.7716    
sexe2                    -0.09590    0.06215  -1.543   0.1228    
permis1                   0.24419    0.17206   1.419   0.1559    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 9333.4  on 6732  degrees of freedom
Residual deviance: 6596.0  on 6715  degrees of freedom
AIC: 6632

Number of Fisher Scoring iterations: 17

The model has a p-value for the overall significance (as indicated by the Wald test) of less than 2e-16, which suggests that the model is highly significant and provides a good fit to the data. Despite this, the large negative intercept and some insignificant predictors imply there may be potential for further refinement to improve predictive power.

For the variables:

Strong Negative Influences: Short trips and education-related trips significantly reduce the likelihood of car usage. Short trips, in particular, have a very strong negative effect. Teenagers also show a strong reduction in the likelihood of car usage.

Strong Positive Influence: The presence of a car (has_car1) has a very strong positive impact on car usage, with a coefficient of +18.8. This suggests that having a car greatly increases the likelihood of its usage. Similarly, living in rural areas also has a positive impact on car usage, indicating a higher likelihood of car usage compared to urban areas.

Moderate Effects: Medium-distance trips and low-income individuals moderately reduce the likelihood of car usage, while medium-income individuals show a slight increase in car usage.

Minimal Impact: Leisure trips (trip_categoryLeisure) and living in suburban areas (urban_areaSuburb) show small, relatively weak effects on car usage. Their coefficients suggest that these variables have little to no impact on car usage compared to the more influential factors.

The variables has_car1 is not statistically significant, as its p-values is >0.05. However, since the stepwise selection process did not exclude it, it is likely retained in the model to avoid reducing its explanatory power or altering its structure, which could lead to the loss of important relationships or an over-simplified model.

Confusion Matrix: Train Set:

Confusion Matrix and Statistics

          Reference
Prediction    0    1
         0 2236  483
         1 1102 2912
                                          
               Accuracy : 0.7646          
                 95% CI : (0.7543, 0.7747)
    No Information Rate : 0.5042          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.5284          
                                          
 Mcnemar's Test P-Value : < 2.2e-16       
                                          
            Sensitivity : 0.6699          
            Specificity : 0.8577          
         Pos Pred Value : 0.8224          
         Neg Pred Value : 0.7255          
             Prevalence : 0.4958          
         Detection Rate : 0.3321          
   Detection Prevalence : 0.4038          
      Balanced Accuracy : 0.7638          
                                          
       'Positive' Class : 0               
                                          

Confusion Matrix: Test Set:

Confusion Matrix and Statistics

          Reference
Prediction    0    1
         0  945  195
         1  485 1259
                                          
               Accuracy : 0.7642          
                 95% CI : (0.7483, 0.7796)
    No Information Rate : 0.5042          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.5276          
                                          
 Mcnemar's Test P-Value : < 2.2e-16       
                                          
            Sensitivity : 0.6608          
            Specificity : 0.8659          
         Pos Pred Value : 0.8289          
         Neg Pred Value : 0.7219          
             Prevalence : 0.4958          
         Detection Rate : 0.3277          
   Detection Prevalence : 0.3953          
      Balanced Accuracy : 0.7634          
                                          
       'Positive' Class : 0               
                                          

Same Conclusion for the confusion matrices for the logit model.the minimal differences in performance between the train and test sets suggest that there is no significant overfitting, as the model generalizes well to unseen data. While the model performs better on Class 1, with higher specificity and positive predictive value, there is room for improvement in detecting Class 0.To address this imbalance, methods such as class balancing or hyperparameter tuning may be beneficial